Trace anomalies and QED in curved space

Abstract

It is shown, for massless QED in a weakly curved background, how to obtain full information about the trace anomaly in perturbation theory, including the “topological” term in the gravitational part of the anomaly. The arguments used follow as straightforward adaptations of those presented recently for λφ 4 theory, and rely on a renormalisation-group analysis combined with strong connections between renormalisability of the curved space theory, finiteness of the energy-momentum tensor, and the use of normal products. The first non-zero α-dependent terms appear at O( α 2) for the topological part, and at O( α 3) for the non-conformal R 2 part of the anomaly. Both values can be deduced via the renormalisation-group arguments from simple flat Feynman diagrams. A direct 3-loop calculation confirms the vanishing of the O( α 2) term in the R 2 anomaly. The analysis follows the scalar theory closely, while being simpler in many places.